Eddington-limited X-ray bursts as distance indicators. I. Systematic trends and spherical symmetry in bursts from 4U 1728-34

We investigate the limitations of thermonuclear X-ray bursts as a distance indicator for the weakly magnetized accreting neutron star 4 U 1728 - 34. We measured the unabsorbed peak flux of 81 bursts in public data from the Roxsi X-Ray Timing Explorer (RXTE). The distribution of peak fluxes was bimodal: 66 bursts exhibited photospherk; radius expansion (presumably reaching the local Eddington limit) and were distributed about a mean bolometric flux of 9.2 × 10^-8 ergs cm^-2 s^-1, while the remaining (non-radius expansion) bursts reached 4.5 × 10^-8 ergs cm^-2 s^-1, on average. The peak fluxes of the radius expansion bursts were not constant, exhibiting a standard deviation of 9.4% and a total variation of 46%. These bursts showed significant correlations between their peak flux and the X-ray colors of the persistent emission immediately prior to the burst. We also found evidence for quasi-periodic variation of the peak fluxes of radius expansion bursts, with a timescale of ≃40 days. The persistent flux observed with RXTE/ASM over 5.8 yr exhibited quasiperiodic variability on a similar timescale. We suggest that these variations may have a common origin in reflection from a warped accretion disk. Once the systematic variation of the peak burst fluxes is subtracted, the residual scatter is only ≃3%, roughly consistent with the measurement uncertainties. The narrowness of this distribution strongly suggests that (1) the radiation from the neutron star atmosphere during radius expansion episodes is nearly spherically symmetric and (2) the radius expansion bursts reach a common peak flux that may be interpreted as a standard candle intensity. Adopting the minimum peak flux for the radius expansion bursts as the Eddington flux limit, we derive a distance for the source of 4.4-4.8 kpc (assuming R_NS = 10 km), with the uncertainty arising from the probable range of the neutron star mass M _NS = 1.4-2 M_⊙.